Symbolic-Numeric Implementation of the Method of Collocations and Least Squares for 3D Navier–Stokes Equations

  • Vasily P. Shapeev
  • Evgenii V. Vorozhtsov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)


The method of collocations and least squares, which was previously proposed for the numerical solution of the two-dimensional Navier–Stokes equations governing steady incompressible viscous flows, is extended here for the three-dimensional case. The derivation of the collocation and matching conditions is carried out in symbolic form using the CAS Mathematica. The numerical stages are implemented in a Fortran code, into which the left-hand sides of the collocation and matching equations have been imported from the Mathematica program. The results of numerical tests confirm the second order of convergence of the presented method.


Stokes Equation Matching Condition Symbolic Computation Computer Algebra System Immerse Boundary Method 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vasily P. Shapeev
    • 1
  • Evgenii V. Vorozhtsov
    • 1
  1. 1.Khristianovich Institute of Theoretical and Applied MechanicsRussian Academy of SciencesNovosibirskRussia

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